A cubical block of side 14 cm is surmounted by a hemisphere . what is the greatest radius that the hemisphere can have?

Answers

Answer 1

Answer:

9.9cm

Step-by-step explanation:

The hemisphere will have its greatest radius along the diagonal of the cube it was surmounted on. The base of the cubical block will be square in nature. Since a cube has all its sides equal, we can find the length of its diagonal using pythagoras theorem as shown.

[tex]hyp^{2} = adj^{2} +opp^{2}[/tex]

Note that the diagonal will be the hypotenuse of the square face which is the longest sides.

Given adjacent = 14cm and opposite = 14cm

[tex]hyp^{2} = 14^{2} +14^{2}\\hyp = \sqrt{196+196} \\hyp = \sqrt{392} \\hyp = 19.8cm[/tex]

The diagonal of the base of the cube is 19.8cm which is equivalent to the greatest diameter of the sphere.

The greatest radius that the hemisphere can have = 19.8/2 = 9.9cm

Answer 2
General Formulas and Concepts:Geometry

Drawing diagrams

Circles

Radius rDiameter dRelationship between r and d:
[tex]\displaystyle r = \frac{d}{2}[/tex]

Cubes

Length lWidth wHeight h

Application:

Let's draw a figure to supplement a visual image to further understand what we need to find. Please refer to the attached image for reference. Please excuse the poor handwriting/drawing. It is also not to scale.

We know that there is a cubical block w/ side measurements of 14 cm. "Surrmounted" means on top. So a hemisphere (half of a sphere) is on top of our block.

If we take a look at our geometrical shape from the top-down angle, we can see that the top would just look like a circle within a square, as depicted in blue.

Labeling our measurements, we can see that the length, width, and height of our cubical block are equal to 14 cm due to the definition of a cube. This extends to the definition of a square as well, so the length and width of our square are also equal to 14 cm.

With the side of the square equal to 14 cm, we know that this is equal to the circle's diameter. So d = 14 cm. We can solve for the radius of the circle/hemisphere by substituting it into the radius formula:

[tex]\begin{aligned}r & = \frac{d}{2} \\& = \frac{14 \ \text{cm}}{2} \\& = \boxed{ 7 \ \text{cm}} \\\end{aligned}[/tex]

Answer:

∴ the greatest radius that the hemisphere can have is equal to 7 cm. Any r > 7 cm would result in the hemisphere being over the edge of the cube.

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Learn more about Geometry: https://brainly.com/question/27732359

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Topic: Geometry

Unit: Composition of Geometrical Shapes

A Cubical Block Of Side 14 Cm Is Surmounted By A Hemisphere . What Is The Greatest Radius That The Hemisphere

Related Questions

Devin’s friend Ryan lives 2 blocks west and 5 blocks south of Devin. Devin’s friend Andy lives 7 blocks east and 2 block north of Devin. How far do Ryan and Andy live from each other?

Answers

Answer:

Answer:

Ryan and Andy live 11.4 blocks from each other.

Step-by-step explanation:Devin’s friend Ryan lives 2 blocks west and 5 blocks south of Devin.Position of Ryan on coordinate system: 2 blocks west (2 unit left from origin) = -2 5 blocks south (5 unit down) = -5Coordinate of Ryan: (-2,-5)Devin’s friend Andy lives 7 blocks east and 2 block north of Devin. Position of Andy on coordinate system: 7 blocks east (7 unit right ) = 7 2 block north (2 unit up) = 2Coordinate of Andy: (7,2)We need to find the distance of Ryan and Andy.

Answer:

C.) 11.4

Step-by-step explanation:

Just took the test on Edge 2020

Can anyone help me solve this equation? 4b+11=39

Answers

The answer is b = 7


Step by step answer

If you expand and simplify (2x+3)(x+4)

Answers

Answer:

The answer is 2x² + 11x + 12.

Step-by-step explanation:

You have apply Distributive Law,

[tex]a(m + n) = am + an[/tex]

So for this question :

[tex](2x + 3)(x + 4)[/tex]

[tex] = 2x(x) + 2x(4) + 3(x) + 3(4)[/tex]

[tex] = 2 {x}^{2} + 8x + 3x + 12[/tex]

[tex] = 2 {x}^{2} + 11x + 12[/tex]

[tex](2x + 3)(x + 4) \\ = 2x(x + 4) + 3(x + 4) \\ = 2x \times x + 2x \times 4 + 3 \times x + 3 \times 4 \\ = {2x}^{2} + 8x + 3x + 12 \\ = {2x}^{2} + 11x + 12 \\ hope \: it \: helps[/tex]

How do I figure out how many combinations there are.

Answers

Answer:

multiplying and dividing

Step-by-step explanation:

What is the midpoint of the segment shown below?

Answers

Answer:

(1, -3/2)

Step-by-step explanation:

The x coordinate is the same for both endpoints so the x coordinate for the midpoint is 1

The y coordinate for the midpoint is found by adding the two y coordinates and dividing by 2

(2+-5)/2 = -3/2

The midpoint is

(1, -3/2)

Answer:

The answer is D

Step-by-step explanation:

Can someone please help me

Answers

Answer:

1) D

2) B

3) A

4) D

Step-by-step Explanation:

1) 1,300,000

= 1.3 × 10⁶

2) 0.052

= 5.2 × 10⁻²

3) 4,500

= 4.5 × 10³

4) 0.00061

= 6.1 × 10⁻⁴

a 4cm by 6cm rectangle sits inside a circle with a radius of 11 cm what is the shaded region

Answers

Answer:

355.94 cm2

Step-by-step explanation:

if it is the area of the shaded part, you have to find the area of rectangle and the area of the circle, then subtract the rectangle's area from the circle's.

area of circle = 3.14( i used this π because the radius is not divisible by 7) × 11 × 11 = 379.94.

area of rectangle = 6 × 4 = 24cm

379.94 - 24.00 = 355.94cm2.

What is the equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (-2, 4)?


Answers

Answer: 5x + 2y = -2

Step-by-step explanation:

Change 5x+2y=12 to slope intercept: 2y = 12 - 5x, y = -5x/2 + 6

A parallel line has the same slope, so the line we try to find is y = -5x/2 + b.

Substitute (-2, 4) in and get 4=5+b, so b = -1.

Therefore the answer is y = -5x/2 - 1, or if you want it in the original form it would be 2y = -5x - 2 ---> 5x+2y = -2.

Hope that helped,

-sirswagger21

If jasmine gets $3.00 every time her song gets 1500 streams how much money would she have if she got 3 million streams

Answers

Answer:

$2000

Step-by-step explanation:

3,000,000/1500=$2000

what is the c value?
answer in x= form

Answers

x form =-1+√21,-1-√21

Given the range {-1, 5, 9), what is the domain for the relation y = x + 3?

Answers

Answer:

yes

Step-by-step explanation:

because it happens that way that it wants

Answer:

The answer is {-4,2,6}

Step-by-step explanation:

I am sorry if i had more time i would explain but i gotta go.

Matías compró un cuarto kilogramo de jamón y lo utilizó para hacer tres tortas así No sobró y a cada torta le puso la misma cantidad de jamón cuánto le tocó a cada torta

Answers

Answer:

The amount of ham in each cake = 1/12 kg

Question:

Matías bought a quarter kilogram of ham and used it to make three cakes like that. There was no leftover and he put the same amount of ham in each cake, how much he touched in each cake.

Step-by-step explanation:

Matías bought = 1/4 kilogram of ham

1/4 kilogram of ham = 3 cakes

There was no remainder

the same amount of ham is in each cake.

To find the amount of ham in each cake, we need to know the fraction of ham in each cake.

Since 3cakes = 1/4kg

1cake = (1/4kg×1cake)/3cakes

= 1/4kg ÷ 3 = 1/4 × 1/3

The fraction of ham in each cake = 1/12

The amount of ham in each cake = 1/12 kg

During the 2010 baseball​ season, the number of wins for three teams was three consecutive integers. Of these three​ teams, the first team had the most wins. The last team had the least wins. The total number of wins by these three teams was 252. How many wins did each team have in the 2010​ season?

Answers

Answer: 83,84 and 85

Step-by-step explanation:

Let the number of win for the teams be x, x+1 and x+2 respectively. From the question, we are told that the total number of wins by these three teams was 252 for the 2010​ season. Therefore,

x+x+1+x+2 = 252

3x+3 = 252

3x = 252 - 3

3x = 249

x = 249/3

x = 83

This means that the team with least wins has 83 while the second team has 84 and the team with most wins has 85.

f(n) = 4(n-1) + 7

fine the first three(3) terms in the sequence show all work​

Answers

........................................

Answer:

f(n) = 4(n-1) + 7

First term

f(1) = 4(1-1) +7 = 0 + 7 = 7

Second term

f(2) = 4(2-1) + 7

= 4(1) + 7 = 4 + 7 =11

Third term

f(3) = 4(3-1) + 7

= 4(2) + 7

= 8 + 7 = 15

Therefore the first three terms of the sequence are 7, 11 and 15.

Hope this helps

Describe fully the single transformation that maps triangle a onto triangle b

Answers

Answer:

reflection of Δa about y=2 results in Δb

Step-by-step explanation:

The single transformation that maps triangle a onto triangle b is: Reflection about y=2

Triangle A should be reflected about y=2 to map it onto Triangle B.

Here, from the given figure we get,

Coordinates of the vertices of triangle (A) are A(1, 3), B(2, 3) and C(1, 5)

After transformation of triangle A, coordinates of the vertices A', B' and C' of the image triangle (B) are,

A'(1, 1), B'(2, 1) and C'(1, -1)

Lets choose point A to find the rule of transformation,

A(1, 3) → A'(1, 1)

Rule → (x, y) → (x, 2 - (y - 2)) or (x, y) → (x, 4 - y)

It shows triangle (A) has been reflected across a line y = 2.

Therefore, Triangle A should be reflected about y=2 to map it onto Triangle B.

To learn more on reflection click:

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#SPJ3

Using the quadratic formula to solve 2x2 = 4x – 7, what are the values of x? 2 plus-or-minus StartRoot 10 EndRoot i 1 plus-or-minus StartRoot 10 EndRoot i StartFraction 2 plus-or-minus StartRoot 10 EndRoot i Over 2 EndFraction 1 plus-or-minus StartRoot 5 EndRoot i

Answers

Answer:

[tex]x = 1 +/- \frac{i\sqrt{10} }{2}[/tex]

Step-by-step explanation:

The equation given is:

[tex]2x^2 = 4x - 7\\\\2x^2 - 4x + 7 = 0[/tex]

Using quadratic formula:

[tex]x = \frac{-b +/- \sqrt{b^2 - 4ac} }{2a}[/tex]

From the question:

a = 2, b = -4, c = 7

Therefore:

[tex]x = \frac{4 +/- \sqrt{(-4)^2 - 4 * 2 * 7} }{2 * 2}\\\\x = \frac{4 +/- \sqrt{(16 - 56)} }{4}\\\\x = \frac{4 +/- \sqrt{-40} }{4}\\[/tex]

=> [tex]x = 1 +/- \frac{i\sqrt{10} }{2}[/tex]

The solution of given quadratic equation is given as   [tex]x = 1 \pm i\dfrac{\sqrt{10}}{2}[/tex]

Given the quadratic equation:

[tex]2x^2 = 4x -7[/tex]

Formula for finding roots of quadratic equation [tex]ax^2 + bx + c = 0[/tex] is given by:

[tex]x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} \\[/tex]

Here, we get a = 2, b = -4, and c = 7.

Thus, the roots can be found as:

[tex]x = \dfrac{4 \pm \sqrt{16 - 56}}{4} \\\\x = \dfrac{4 \pm \sqrt{-40}}{4} \\\\x = \dfrac{4 \pm 2i\sqrt{10}}{4} \\\\\\x = 1 \pm i\dfrac{\sqrt{10}}{2}[/tex]

Thus, the solution of the given quadratic equation is given as  [tex]x = 1 \pm i\dfrac{\sqrt{10}}{2}[/tex].

Learn here more:

https://brainly.com/question/4366363

Please help! select the correct answer

Answers

Answer:

the answer is show me your kitty cat

Step-by-step explanation:

If (x - 3) represents the side of a cube, what is the
polynomial that represents its volume?​

Answers

Answer:

x³ - 9x² + 27x - 27

Step-by-step explanation:

The volume (V) of a cube is calculated as

V = s³ ( s is the measure of the side ) , thus

V = (x - 3)³

   = (x - 3)(x - 3)(x - 3) ← expand the second/ third factors using FOIL

   = (x - 3)(x² - 6x + 9) ← distribute

   = x³ - 6x² + 9x - 3x² + 18x - 27 ← collect like terms

   = x³ - 9x² + 27x - 27

20% of a number is 58

Answers

Answer:

290

Step-by-step explanation:

The reason this is the answer is because if you divide 100% by 20% it will give you 5% so then you have to multiply 58 times 20 which will give you 290.

Answer:

290

Step-by-step explanation:

A and B are two similar solids.
15 cm
10 cm
The volume of A is 400 cm.


Work out the volume of B.
Similarity - Area and Volume
View One Minute Version
Overview

Answers

Answer:

600cm3 the 3 is ment to be cubed

Step-by-step explanation:

A 350 m cable is attached to the top of the tower. The angle of elevation to the top of the tower is 60. How high is the tower in meters

Answers

Answer:

303

Step-by-step explanation:

sin 60 = x / 350

x = 350(sin60) = 303.1

The price of a gallon milk was $2.65 the price rose why dollars after the last hurricane then the price dropped $.15 and later Rosie came by five cents which expression represents the current price of milk

Answers

Answer:

p =  y + 2.55

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  

Please have a look at the attached photo.  

The price of a gallon of milk was $2.65. The price rose y dollars after the last hurricane. Then the price dropped $0.15 and later rose again by $0.05. Which expression represents the current price of milk

My answer:

Let p is the price of milk

Given the information:

Stage 1: The price of a gallon milk was $2.65

<=> p = 2.65  

Stage 2: rose y dollar

<=> p = 2.65   + y

Stage 3:  price dropped $.15

<=> p =  2.65   + y  - 0.15

Stage 4: rose again by $0.05

<=> p = 2.65  + y  - 0.15  + 0.05

<=> p =  y + 2.55

Hope it will find you well.

What is d, the common difference, in the arithmetic sequence 100, 98, 96, 94, 92, ...?
-1
Ο 2
Ο Ο Ο Ο.
-2
Ο 100

Answers

Answer:

-2

Step-by-step explanation:

State the solution
5x-y=14 and x+3y=-10

Answers

Answer:

x = 2, y = - 4

Step-by-step explanation

5x-y=14

x+3y= - 10

x = - 10 - 3y

5(- 10 - 3y) - y = 14

- 50 - 15y - y = 14

-16y = 64

y = - 4

x = -10 - 3y = - 10 - 3*(- 4) = - 10 + 12 = 2

x = 2

plz hurry and answer i will give brainliest

what is 2*2+6/2*3

Answers

Answer:

This would equal 13.

2x2=4, 6/2=3, 3x3=9, 9+4=13

if f(x) =5x-2 and g(x) = 2x +1 find(f+g)(x)

Answers

Answer & Step-by-step explanation:

When we see (f + g)(x), it means that we are going to be adding f(x) to g(x).

f(x) = 5x - 2

g(x) = 2x + 1

(f + g)(x) = (5x - 2) + (2x + 1)

Combine like terms.

(f + g)(x) = 7x - 1

So, (f + g)(x) equals 7x - 1

the mean of the data set {9, 5, y, 2, x } is twice the data set {8, x, 4, 1, 3}. What is (y-x)^2?​

Answers

Answer:

256

Step-by-step explanation:

To calculate the mean, we simply divide the sum of the values by the count.

For the first set, the mean is as follows;

(9 + 5 + 2 + y + x)/5 = (x + y + 16)/5

For the second set;

(8 + x + 4 + 1 + 3)/5 = (16 + x)/5

Since both are divided by 5, we can eliminate it

Mean of first set is twice the second

This means that;

x + y + 16 = 2(16 + x)

x + y + 16 = 32 + 2x

y = 32-16+2x-x

y = 16 + x

Now we want to calculate

(y-x)^2

substitute the value of y here

(16+x-x)^2

= 16^2 = 256

Predecessor and successor of 999​

Answers

Can u give me an example of the problem

How can a triangular prism have a greater volume than a rectangular prism?

Answers

Answer:

If the triangular prism is bigger than the rectangular prism, it will have a greater volume. There are also many other reasons listed below:

Possible reasons:

If the triangular prism is bigger than the rectangular prism, it will have a greater volumeThe rectangular prism could have less width than the triangular prismThe rectangular prism could have less depth than the triangular prismThe rectangular prism could have less length than the triangular prism

Please mark Brainliest if correct.

Sorry if it is not correct.

The volume of a triangular prism is less than a rectangular prism with the same size base. A painter would need to know the surface area hope it helps

Solve for x. Assume that line which appear to be diameters are actual diameters.

Answers

Answer:

x = 8

Step-by-step explanation:

The angle above the 6x-8 = 180 -140 = 40

The angle on the opposite side is 40 degrees as well because they are vertical angles

6x-8 = 40 degrees

Add 8 to each side

6x= 48

Divide by 6

6x/6 = 48/6

x = 8

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